Solution Strategies for Nonlinear Multiscale Multipatch Problems with Application to Analysis of Local Singularities

Yaxiong Chen, Purdue University

Abstract

Many Engineering structures, including electronic component assemblies, are inherently multi-scale in nature. These structures often experience complex local nonlinear behavior such as plasticity, damage or fracture. These local behaviors eventually lead to the failure at the macro length scale. Connecting the behavior across the length scales to develop an understanding of the failure mechanism is important for developing reliable products. To solve multi-scale problems in which the critical region is much smaller than the entire structure, an iterative solution approach based on domain decomposition techniques is proposed. Two independent models are constructed to model the global and local substructures respectively. The unbalanced force at the interface is iteratively reduced to ensure force equilibrium of the overall structure in the final solution. The approach is non-intrusive since only nodal values on the interface are transferred between the global and local models. Solution acceleration using SR1 and BFGS updates is also demonstrated. Equally importantly, the two updates are applied in a non-intrusive manner, meaning that the technique is implemented without needing access to the codes using which the sub-domains are analyzed. Code- and mesh-agnostic solutions for problems with local nonlinear material behavior or local crack growth are demonstrated. Analysis in which the global and local models are solved using two differentcommercial codes is also demonstrated. Engineering analysis using numerical models are helpful in providing insight into the connection between the structure, loading history, behavior and failure. Specifically, Isogeometric analysis (IGA) is advantageous for engineering problems with evolving geometry compared to the traditional finite element method (FEM). IGA carries out analysis by building behavioral approximations isoparametrically on the geometrical model (commonly NURBS) and is thus a promising approach to integrating Computer-Aided Design (CAD) with Computer-Aided Engineering (CAE). In enriched isogeometric Analysis (EIGA), the solution is enriched with known behavior on lower dimensional geometrical features such as crack tips or interfaces. In the present research, enriched field approximation techniques are developed for the application of bound ary conditions, coupling patches with non-matching discretizations and for modeling singular stresses in the structure. The first problem solution discussed is to apply Dirichlet and Neumann boundary conditions on boundary representation (B-rep) CAD models immersed in an underlying domain of regular grid points. The boundary conditions are applied on the degrees of freedom of the lower dimensional B-rep part directly. The solution approach for the immersed analysis uses signed algebraic level sets constructed from the B-rep surfaces to blend the enriched field with the underlying field. The algebraic level sets provide a surrogate for distance, are non-iteratively (or algebraically) computed and allow implicit Boolean compositions. The methodology is also applied to couple solution approximations of decomposed patches by smoothly blending incompatible geometries to an arbitrary degree of smoothness. A parametrically described frame or interface is introduced to “stitch” the adjacent patches. A hierarchical blending procedure is then developed to stitch multiple unstructured patches including those with T-junctions or extraordinary vertices. Finally, using the EIGA technique, a computational method for analyzing general multimaterial sharp corners that enables accurate estimations of the generalized stress intensity factors is proposed. Explicitly modeled geometries of material junctions, crack tips and deboned interfaces are isogeometrically and hierarchically enriched to construct approximations with the known local behavior.

Degree

Ph.D.

Advisors

Subbarayan, Purdue University.

Subject Area

Mathematics|Polymer chemistry

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